1. Introduction

Computer graphics and visualization deal with preparing data in order to show (“visualize“) these data on a (two-dimensional) computer screen. In computer graphics, the original data typically stem from the three-dimensional Euclidean space R3, whereas in scientific visualization the data might originate from spaces of much higher dimension (e.g., in information visualization or high-dimensional sphere models in statistical mechanics) [Swayne et al. 1998].

In these scenarios, visibility computations play a central role [O'Rourke 1997]. In the simplest case, we are given a fixed viewpoint υ ∈ ℝ n, and the scene consists of a set B of bodies. Now the task is to compute a suitable two-dimensional projection of the scene (“to render the scene“) that reflects which part of the scene is visible from the viewpoint υ;. Ina more dynamic setting, the viewpoint can be moved interactively (see [Bern et al. 1994; Lenhof and Smid 1995], for example). However, in general, after each movement of the viewpoint a new rendering process is necessary. In order to speed up this process, commercial Tenderers apply caching techniques [Wernecke 1994].